Write the slope-intercept equation for the line that passes through (-9, 9) and is perpendicular to -9x – 2y = 10 Please show all of your work.

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academicsfirst's profile pic

academicsfirst | High School Teacher | (Level 2) Adjunct Educator

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This method will use y = mx + b to find the equation instead of the point-slope method.

We are being asked to find the equation of a line perpendicular to -9x -2y = 10 that passes through the point (-9,9).

We will first find the slope of the perpendicular line by transforming the given equation into slope-intercept form which is y = mx + b.

-9x-2y = 10

-2y = 9x + 10

y = -9/2x - 5

The slope of a line perpendicular to the given equation will be 2/9 which is the "opposite reciprocal" of -9/2.

Now we will use direct substitution into y = mx +b to find the y intercept of the new equation.

y = mx + b

9 = 2/9(-9) + b

9 = -2 + b

11= b

Now, write the equation in slope-intercept form using the slope 2/9 and the y intercept 11.

The equation of the line that is perpendicular to the given line and containing the given point is y = (2/9)x + 11.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The slope-intercept form of the equation of a line is y = mx + c where m is the slope and c is the y-intercept.

The line given to us -9x - 2y = 10 can be written in the slope-intercept form as

-2y = 9y + 10

=> y = (-9/2)x - 5

The slope of the line is -9/2. As the product of the slope of two perpendicular lines is -1, the slope of the required line is 2/9.

The required line passes through (-9, 9). We get the equation:

(y - 9)/(x + 9) = 2/9

=> y - 9 = 2x/9 + 2*9/9

=> y = (2/9)x + 2 + 9

=> y = (2/9)x + 11

The equation of the required line is y = (2/9)x + 11

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

Write the slope-intercept equation for the line that passes through (-9, 9) and is perpendicular to -9x – 2y = 10 Please show all of your work.

-9x - 2y = 10

-9x - 10 + 2y 

y = (-9/2)x - 5

The slope of this equation is -9/2. The slope of the perpendicular line is 2/9 (The negative reciprocal. 

 The slope-intercept looks like this: y = mx + b 
 
To get to this, using the point-slope formula will make it easier: y - y1 = m(x - x2)
 
y - 9 = 2/9 (x + 9)
 
Get y by itself:
y = (x2/9) + 11

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